A Dialectica Model of State

Reddy 13] introduced an extended intuitionistic linear calculus to model some features of state-manipulation. His calculus LLMS { for Linear Logic Model of State { includes the connective \before" and an its associated modality y. De Paiva 5] presents a (collection of) dialectica categorical models for Classical Linear Logic, the categories GC. These categories contain an extra tensor product functor and a comonad structure corresponding to a modality related to it. It is surprising that these works arising from completely diierent motivations can be related in a meaningful way. In this paper we present a dialectica category G which models the sequent calculus LLMS c , the commutative version of Reddy's LLMS. Furthemore, we present a computational characterization of the fragment ff; ; &g of LLMS c in the framework of CSP 9]. We draw some preliminary conclusions and point out extensions and future work. extens~ oes e trabalhos futuros.